US12158447B2ActiveUtilityPatentIndex 39
Wear monitoring method of polymer thrust bearing based on ultrasonic reflection coefficient amplitude spectrum (URCAS)
Est. expirySep 23, 2042(~16.2 yrs left)· nominal 20-yr term from priority
G01M 13/04F16C 2233/00F16C 41/00F16C 33/20F16C 17/04G01N 29/043Y02E30/30G06N 3/006G01B 17/02G01N 29/07
39
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0
Cited by
13
References
7
Claims
Abstract
A wear monitoring method of a polymer thrust bearing based on an ultrasonic reflection coefficient amplitude spectrum (URCAS), includes: selecting a corresponding delay block probe based on a material of a to-be-tested bearing, and setting corresponding parameters of a pulse generator; after collecting a primary echo from a surface of the delay block probe as a reference signal, placing the delay block probe in a designated region on a back of the to-be-tested bearing, and collecting time-domain echo signals from upper and lower surfaces of the bearing; establishing a propagation model of an ultrasonic signal in a polymer bearing, and calculating a theoretical URCAS based on the propagation model; calculating a measured URCAS; and constructing an objective function, and solving the objective function by using a differential evolution algorithm. A plurality of parameters of the polymer bearing is solved to meet a requirement for wear monitoring by adopting the method.
Claims
exact text as granted — not AI-modifiedWhat is claimed is:
1. A wear monitoring method of a polymer thrust bearing based on an ultrasonic reflection coefficient amplitude spectrum (URCAS), comprising following steps:
selecting a corresponding delay block probe based on a material of a to-be-tested bearing, setting corresponding parameters of a pulse generator, connecting the delay block probe to the pulse generator, and connecting the pulse generator to a digital oscilloscope;
after collecting a primary echo from a surface of the delay block probe as a reference signal, placing the delay block probe in a designated region on a back of the to-be-tested bearing, and collecting time-domain echo signals from upper and lower surfaces of the bearing;
establishing a propagation model of an ultrasonic signal in a polymer bearing, and calculating a theoretical URCAS based on the propagation model;
calculating a measured URCAS based on the time-domain echo signals collected from the upper and lower surfaces of the bearing; and
constructing an objective function based on the measured URCAS and the theoretical URCAS to represent a similarity between measured echo data and theoretical calculated echo data, and solving the objective function by using a differential evolution algorithm, wherein when a correlation coefficient is largest and a root-mean-square error is smallest, a similarity between the measured URCAS and the theoretical URCAS is largest, and in this case, independent variables corresponding to the objective function are parameters of the polymer bearing; wherein
during calculation of the theoretical URCAS, a reflection coefficient R of a polymer layer is expressed as follows:
R
=
P
1
+
P
2
P
1
=
r
1
2
+
t
1
2
r
2
3
t
2
1
exp
(
-
2
α
d
)
cos
(
4
π
fd
c
2
)
r
1
2
+
i
t
1
2
r
2
3
t
2
1
exp
(
-
2
α
d
)
sin
(
4
π
fd
c
2
)
r
1
2
the reflection coefficient R of the polymer layer is a complex number, a modulus of the reflection coefficient is a function of a frequency, and the function is referred to as the URCAS, which is expressed as follows:
R
(
f
)
=
{
[
r
1
2
2
+
2
r
1
2
r
2
3
(
1
-
r
1
2
2
)
exp
(
-
2
α
d
)
cos
(
4
π
fd
c
2
)
+
r
2
3
2
(
1
-
r
1
2
2
)
2
exp
(
-
4
α
d
)
]
/
r
1
2
2
}
an attenuation coefficient of the polymer layer is expressed as follows:
α
(
f
)
=
1
2
d
ln
[
(
1
-
r
1
2
2
)
r
2
3
A
1
(
f
)
r
1
2
A
2
(
f
)
]
=
1
2
d
ln
[
w
·
A
1
(
f
)
A
2
(
f
)
]
wherein A 1 (f) and A 2 (f) respectively represent amplitude spectra of reflection echoes on upper and lower interfaces of the polymer layer, and w represents an attenuation factor.
2. The wear monitoring method according to claim 1 , wherein the setting corresponding parameters of the pulse generator comprises setting a pulse repetition frequency (PRF), pulse energy, a damping, a gain, and a filter bandwidth.
3. The wear monitoring method according to claim 1 , wherein when the propagation model of the ultrasonic signal in the polymer bearing is established, the bearing is simplified into a homogeneous and smooth layered material, a medium I is a delay block, a medium II is a layered polymer material, a medium III is air or water, acoustic impedance of the medium I, the medium II, and the medium III is Z 1 , Z 2 , and Z 3 respectively, the acoustic impedance is numerically equal to a density of the medium multiplied by a sound velocity, and when an ultrasonic pulse wave with a sound pressure of 1 and a frequency of f is perpendicularly incident into a three-layer medium along a negative direction of a z axis, a received reflected wave is expressed as follows:
{
P
1
=
r
1
2
P
2
=
r
2
3
t
1
2
t
2
1
exp
(
2
i
k
2
z
d
)
P
3
=
r
2
3
2
t
1
2
r
2
1
t
2
1
exp
(
4
i
k
2
z
d
)
……
P
n
=
r
2
3
n
t
1
2
r
2
1
n
-
1
t
2
1
exp
[
2
(
n
-
1
)
i
k
2
z
d
]
,
k
2
z
=
2
π
f
c
2
+
i
α
wherein P 1 represents the reflected echo of the upper interface of the polymer layer, P 2 represents a sound wave transmitted into the polymer layer and transmitted from the upper interface after being reflected once on the lower interface, P 3 represents a sound wave transmitted into the polymer layer and transmitted from the upper interface after being reflected twice on the lower interface, P n represents a sound wave transmitted into the polymer layer and transmitted from the upper interface after being reflected n times on the lower interface, r 12 and r 23 respectively represent reflection coefficients of the polymer layer when an ultrasonic wave is propagated to interfaces 1 and 2 along the negative direction of the z axis, r 21 represents a reflection coefficient of the polymer layer when the ultrasonic wave is propagated to the interface 1 along a positive direction of the z axis, t 12 and t 21 respectively represent coefficients of transmitting the sound pressure along different directions on the interface 1 , n represents a quantity of reflection echoes, d and c 2 respectively represent a thickness and a sound velocity of the polymer layer, α represents the attenuation coefficient of the polymer layer, k 2z represents a quantity of waves along a z direction in the polymer layer, exp (2ik 2z d) represents a phase change of the sound wave after one round trip in the polymer layer, exp (4ik 2z d) represents a phase change of the sound wave after two round trips in the polymer layer, and exp(2(n−1)k 2z d) represents a phase change of the sound wave after (n−1) round trips in the polymer layer.
4. The wear monitoring method according to claim 1 , wherein when the measured URCAS is calculated, zero filling and fast fourier transform (FFT) are performed on the reference signal collected from the delay block probe to obtain a frequency-domain amplitude spectrum, a bandwidth at −6 dB of the frequency-domain amplitude spectrum is intercepted as an effective frequency band, time-domain separation, the zero filling, and the FFT are sequentially performed on reflected waves collected from the upper and lower surfaces of the polymer bearing to obtain an amplitude spectrum A 12 (f) of the upper and lower interfaces, the amplitude spectrum A 1 (f) of the upper interface, and the amplitude spectrum A 2 (f) of the lower interface, and then the measured URCAS R(f) is calculated according to the following formula:
R
(
f
)
_
=
A
1
2
(
f
)
A
1
(
f
)
.
5. The wear monitoring method according to claim 1 , wherein when the objective function is constructed to represent the similarity between the measured echo data and the theoretical calculated echo data, the correlation coefficient and the root-mean-square error are selected as the objective function to measure the similarity between the theoretical URCAS and the measured URCAS, and the correlation coefficient reflects a similarity between change trends of the measured and the theoretical calculated echo data, and a formula of the URCAS is substituted to obtain an expression of the correlation coefficient:
r
p
(
c
2
,
d
,
ρ
,
w
)
=
∑
i
=
1
N
[
R
(
f
;
c
2
,
d
,
ρ
,
w
)
-
R
(
f
;
c
2
,
d
,
p
,
w
)
_
]
[
R
(
f
;
c
2
,
d
,
ρ
,
w
)
*
-
R
(
f
;
c
2
,
d
,
ρ
,
w
)
*
_
]
∑
i
=
1
N
[
R
(
f
;
c
2
,
d
,
ρ
,
w
)
-
R
(
f
;
c
2
,
d
,
p
,
w
)
]
2
∑
i
=
1
N
[
R
(
f
;
c
2
,
d
,
ρ
,
w
)
*
-
R
(
f
;
c
2
,
d
,
ρ
,
w
)
*
_
]
2
wherein N represents a quantity of data points within a frequency domain range after the FFT is performed on a time-domain signal; subscript i represents an i th frequency value; R(f;c 2 , d, ρ, w) and R(f;c 2 , d, ρ, w)* respectively represent a measured URCAS and a theoretical URCAS within an effective frequency band; and R(f;c 2 , d, ρ,w) and R(f;c 2 , d, ρ,w)* respectively represent arithmetic mean values of the measured URCAS and the theoretical URCAS within the effective frequency band, and ρ represents a density of the polymer layer;
the root-mean-square error is introduced as a second constraint, which reflects numerical consistency of the measured and the theoretical calculated echo data, and an expression of the root-mean-square error is obtained by substituting the measured URCAS R(f;c 2 , d, ρ,w) and theoretical URCAS R(f;c 2 , d, ρ,w)*:
RMS
E
=
1
N
∑
i
=
1
N
[
R
(
f
;
c
2
,
d
,
ρ
,
w
)
-
R
(
f
;
c
2
,
d
,
ρ
,
w
)
*
]
2
when the correlation coefficient is the largest and the root-mean-square error is the smallest, the similarity between the measured URCAS and the theoretical URCAS is the largest, and in this case, the independent variables corresponding to the objective function are the parameters of the polymer bearing.
6. The wear monitoring method according to claim 1 , wherein the solving the objective function by using the differential evolution algorithm comprises:
initialization: randomly initializing a population in solution space of a to-be-solved parameter;
differential mutation: under a Rand mutation strategy, performing differential scaling on a randomly generated sub-individual to produce a mutation vector;
crossover: performing a crossover operation by using a binomial step-by-step crossover operator to generate a test vector;
selection: comparing fitness of a test individual and a parent individual by using a greedy selection strategy, and preserving an individual with best fitness in a new-generation population; and
determining: determining an evolution termination condition, and reaching a maximum quantity of evolution generations or obtaining an optimal solution.
7. The wear monitoring method according to claim 6 , wherein when the objective function is solved by using the differential evolution algorithm,
for the constructed objective function, the differential evolution algorithm randomly generates a population {X 1,g , X 2,g , . . . , X NP,g } containing NP feasible solutions, wherein g represents a quantity of evolution generations, NP represents a quantity of feasible solutions, and X represents a representation symbol of the individual in the population; an individual X j,g =(x 1,g j , x 2,g j , . . . x D,g j ) in the population is used to represent a solution of a problem, wherein D represents a quantity of dimensions of an optimization variable, and g represents the quantity of evolution generations; and each individual is uniformly and randomly determined within a range of [X min , X max ], wherein X min =(x min 1 , x min 2 , . . . , x min D ), X max =(x max 1 , x max 2 , . . . , x max D ), and a series of random individuals constitute an initial population, which is expressed by the following formula:
x i j =x min j +rand (0,1)·( x max j −x min j ), j∈[ 1, D]
wherein rand (0,1) represents a real number that is uniformly and randomly determined between 0 and 1;
the differential evolution algorithm realizes individual mutation based on a differential strategy, randomly selects two different individuals in the population based on a classic mutation strategy, and then scales a vector difference of the two different individuals to perform vector synthesis with the to-be-mutated individuals, wherein the generated mutation vector V i,g is expressed by the following formula:
V i,g =X a,g +F ·( X b,g −X c,g ), a≠b≠c≠i
wherein X a,g , X b,g , and X c,g represent three randomly selected individuals in the population, and F represents a scaling factor;
the differential evolution algorithm introduces the crossover operation, such that at least one component of the test vector comes from the mutation vector, as shown in the following formula:
U
i
,
g
+
1
=
{
V
i
,
g
j
,
if
(
rand
j
(
0
,
1
)
≤
CR
)
or
(
j
=
j
r
a
n
d
)
X
i
,
g
j
,
otherwise
wherein rand j (0,1) represents a uniform random number between 0 and 1 in a j th calculation, CR represents a crossover probability within a range of [0, 1], the index j rand represents a randomly selected quantity of dimensions to ensure that the test vector U i,g+1 obtains at least one element from U i,g , and the crossover operation is referred to as binomial uniform crossover;
the differential evolution algorithm selects the greedy selection strategy, and compares an individual generated through the mutation and crossover operations and a parent individual of the generated individual, wherein an individual performing well enters a next-generation population, which is expressed by the following formula:
X
i
,
g
+
1
=
{
U
i
,
g
+
1
,
if
f
(
U
i
,
g
+
1
)
<
f
(
X
i
,
g
)
X
i
,
g
,
otherwise
,
i
=
1
,
2
,
…
,
NP
after mutation, crossover, and selection operations, new individuals next-generation population are generated in a same form and a same number for the next-generation population, a previous-generation population continues to cycle until the termination condition is met, and an optimal result is an obtained thickness parameter of the bearing.Cited by (0)
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